Gauge-invariant neural networks for quantum many-body dynamics

The dynamics of many-body systems is typically accompanied by the growth of entanglement. This imposes limitations on system size and evolution time for many existing numerical methods. On the other hand, neural network wavefunctions have demonstrated the capability to describe some volume law states phases, in principle making them a suitable ansatz for simulating long-time evolution. When dealing with systems (e.g., lattice gauge theories) featuring exact or approximate gauge symmetry, enhancing neural networks with this symmetry can significantly enhance their performance. In this study, we investigate the quench dynamics of a toric code under a perturbed Hamiltonian with gauge symmetry persisting throughout the evolution. We attempt to overcome restrictions in both evolution time and system size by harnessing gauge-invariant neural networks.